The following is a paper that has been written for a Pathfinder home brew new class of armor. Criticism and peer review of it are welcome, and if it does work as a home brew idea, perhaps it should be submitted to Paizo to be adapted officially. Again, though, that's up to all of you.
Sincerely,
Pseudonymus.
A Proposal for a New Type of Alloyed Armor-Plate
by Pseudonymus
April 25, 2014, Please convert to the Golarion calendar
1. Introduction:
This is the scientific working for stats for a suit of plate armor made out of an Adamantine-Mithrill alloy. As it has been discovered by the Author of this paper that there are two metals, namely Adamantine and Mithrill, that have been seen by said Author only in three other universes, but has never seen an alloy made of them, despite the fact that the strengths of metal alloys being superior to pure metals alone in various cases, is known on a great number of worlds in a great many universes, it was determined that an investigation was warranted to determine what the physical characteristics would be of such an alloy, whether it would make a reasonably competitive and comparable suit of armor, and then to determine if its cost would be reasonable on the World of Golarion. The working and analysis is below.
2. Stats for current full plate armor in Pathfinder:
Full steel plate-weight of 50 lbs, hardness of 10
Adamantine-40 hp hardness of 20, full plate set of adamantine, hardness of 20, 1500+15000=16,500 gold weight of 50lbs
Mithrill-Lighter than steel, hardness of 15. Full plate=25lbs cost 10, 5000 gold
3. Physical Statistics for Steel and Calculations of New Statistics for Adamantine and Mithrill:
Density of Steel-7.85g/cm^3.
50 lbs=22.6796 kg=22679.6 g
22679.6/7.85=2889.1210 cm^3=176.30 in^3=31.4414 in^2
Average yield strength of steel armor plate-178 ksi (kilopounds per square inch)
178 ksiX31.4414 si=5596.5692 kilopounds=hardness 10
assuming same average square inch surface area for all types of full plate armor, we can extrapolate as follows:
Mithrill-hardness 15=10+5=10+50%=5596.5692+(5596.5692X0.5)=5596.5692+2798.2846=8394.8538 kilopounds.
8394.8538 kilopounds/31.4414 si=243.74 ksi
25lbs=11.3398 kg=11339.8 g
11339.8 g/2889.1210 cm^3=3.93 g/cm^3
Density of Mithrill-3.93 g/cm^3
Average yield strength of Mithrill-243.74 ksi
Adamantine hardness=2X10=20=5596.5692X2=11193.1384 kilopounds
11193.1384 kilopounds/31.4414 si=356 ksi
Density of Adamantine, owing to same mass and volume is identical to that of steel.
4. Calculations for the Adamantine-Mithrill Alloy and Suit of Plate Armor made from it:
The higher yield strength of Adamantine can be attributed to a combination of a triangular lattice arrangement, with shorter bonds than atoms in steel, and the higher temperatures and cooling processes they undergo being exposed to high radiation areas and the cold of the vaccuum of space.
Turning pure titanium, which has a yeild strength of 434 mpa into an alloy with 0.25% iron yields a tensile strength of 1000 mpa or 154 ksi.
Since 356 ksi is approximately 2454.5342 mpa, an adamantine-mithrill alloy, with 0.25% mithrill should have an approximate strength of 2453.5342+(1000-434)=2454.5342+566=3020.5342 mpaX0.1450377=438.0913 ksi=(438.0913-356)/356%+356=20+23.06%=20+4.6119=Hardness of 24.6118, which rounded up gives a hardness of 25.
Mass of the alloy is, via percent by weight. 7.85 g/cm^3X (0.9975X2889.1210 cm^3)=7.85 g/cm^3 X 2881.8981 cm^3=22,622.9009 g + (3.93 g/cm^3 X (0.0025X 2889.1210 cm^3)=22,622.9009 g+ (3.93 g/cm^3 X 7.2228 cm^3)=22,622.9009 g + 28.3856 g=22651.2865 g=22.6512865 kg=49.9375 lbs which rounds up to 50 lbs.
Final stats for a Adamantine-Mithrill alloy armor. 50 lbs, hardness 25.
Based on the building and r&d, a suit of plate armor made from an adamantine-mithrill alloy should run for about 25,000 gold.
5. Discussion:
Please understand that most of these calculations were based on averages, online conversion calculators for conversion between units, and figures were rounded up to whole numbers when necessary, but it was otherwise attempted to keep all figures to four significant figures. Also, please understand that this is based on as purely a scientific attempt as possible. The magic energies of Universe Sector 02179 (Golarion and the Pathfinder Universe) may make things radically different, and various other factors such as imbuement of magical energies, or different forging techniques may yield different results. The final figures for this alloy in terms of physical statistics make some assumptions about the features of Adamantine, that alloys would work the same way for it and Mithrill like they would for Titanium and iron, and also assume a standard forging process with a high degree of precision chemistry involved. Other forging techniques may yield varying results. If assumptions are accurate, then this is an approximately accurate assessment. Owing to insufficient data about the variance of strength of both adamantine and mithrill, precise variances and confidence intervals could not be established pertaining to the mean strength of the alloy or the plate armor made from it. If pure magic gets involved as well, anything could happen and throw this analysis off. As for the cost of the new armor, the standard manufacturing costs and the cost of the materials should round up the cost to 20,000 gold, but the degree of highly skilled labor in making a precise alloy would require a higher cost added on, so hence a fudge factor of 5000 additional gold, making the cost 25,000 gold. Please understand this is an arbitrary postulation of the cost, owing to severe lack of knowledge of the actual cost of highly skilled labor on Golarion, making this estimate wildly imprecise.
6. Conclusion:
An adamantine-mithrill alloy armor can be made of roughly the same weight as both steel and adamantine armor, with a reasonably higher hardness and strength. Such armor apparently has not been used in any world where both Adamantine and Mithrill exist that the Author has traveled to. However, the reasons as to why this is the case are beyond the scope of this paper and are perhaps grounds for further study.
7. References:
Standard Pathfinder rule books were used for original stats of the armor types in terms of pricing, weight and hardness stats.
This reference gives the density of steel:
http://hypertextbook.com/facts/2004/KarenSutherland.shtml
The average yield strength for armor steel was averaged across the first four types of plate armor referenced here:
http://www.steelwarehouseplate.com/Armor-Plate.81.0.html
Google was used to convert between pounds and kilograms.
The conversion between mpa and ksi was done here:
http://www.tiniusolsen.com/resource-center/mpa-ksi.html
Google was used to convert between cubic centimeters and cubic inches. However, conversion from cubic inches to square inches was done here:
http://www.endmemo.com/cconvert/in3in2.php
Titanium alloy figures for tensile strength were of Grade 5 titanium alloy referenced here:
http://en.wikipedia.org/wiki/Titanium_alloy
And the reference for commercially pure, normal titanium was referenced here:
http://en.wikipedia.org/wiki/Titanium
Finally, this reference talks about the crystalline nature of metals and how this relates to brittleness or ductility:
http://www.scienceforums.net/topic/79549-ductile-and-brittle-metals-vs-crys tal-structure/
